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Journal of Convex Analysis 14 (2007), No. 2, 297--317
Copyright Heldermann Verlag 2007

Positive Sets and Monotone Sets

Stephen Simons
Dept. of Mathematics, University of California, Santa Barbara, CA 93106-3080, U.S.A.

We show how convex analysis can be applied to the theory of sets that are "positive" with respect to a continuous quadratic form on a Banach space. Monotone sets can be considered as a special case of positive sets, and we show how our results lead to very efficient proofs of a number of results on monotone sets. One of the key techniques that we use is a generalization of the Fitzpatrick function from monotone set theory to an analogous function for positive sets.

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